On SIC-POVMs and MUBs in Dimension 6

By M. Grassl. 2004

169 citations recorded by the source corpus.

We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions. An algebraic description of a SIC-POVM in dimension six is given. Furthermore it is shown that several sets of three mutually unbiased bases in dimension six are maximal, i.e., cannot be extended.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f59e978442e79b63309d91cb9f698d8c923a9d3d

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In Artificial Intelligence

In Electrical and Electronic Engineering

In Geometry and Topology

Citations in the corpus

A Concise Guide to Complex Hadamard Matrices (2005, background): “The problems a)-c) are equivalent in the sense that given a solution to one problem one can find a solution to the other one, as well as a corresponding scheme of teleportation or dense coding [43].”
Quantum-Bayesian Coherence (2009, background): “ prime number, and they are generally believed not to exist in other dimensions. For instance, in d= 6 no more than three mutually unbiased basis have ever been found, even after quite extensive work [81, 111, 112, 113], whereas a total of seven are needed for Eq. (65) to be true. The other problem ”
Tight informationally complete quantum measurements (2006, background): “Analytical constructions, however, are known only for d ≤ 10 and d = 12, 13, 19 [24, 27, 47, 48, 49, 50].”
On Weyl-Heisenberg orbits of equiangular lines (2008, background): “The relevance of the (extended) Clifford group to the set of equiangular lines arising from GP(d) has been discussed by several authors (for example see [2, 10]).”
Construction, classification and parametrization of complex Hadamard matrices (2011, methodology): “During our construction we have used various Gröbner bases techniques [20] similar in spirit to [10], [52] and [58], and performed the required calculations with the aid of MAPLE and Mathematica.”